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The superior performance of ensemble methods with infinite models are well known. Most of these methods are based on optimization problems in infinite-dimensional spaces with some regularization, for instance, boosting methods and convex…
Functional lifting methods provide a tool for approximating solutions of difficult non-convex problems by embedding them into a larger space. In this work, we investigate a mathematically rigorous formulation based on embedding into the…
We provide several applications of Optimistic Mirror Descent, an online learning algorithm based on the idea of predictable sequences. First, we recover the Mirror Prox algorithm for offline optimization, prove an extension to Holder-smooth…
We propose Mirror Descent Optimal Transport (MDOT), a novel method for solving discrete optimal transport (OT) problems with high precision, by unifying temperature annealing in entropic-regularized OT (EOT) with mirror descent techniques.…
A major limitation of online algorithms that track the optimizers of time-varying nonconvex optimization problems is that they focus on a specific local minimum trajectory, which may lead to poor spurious local solutions. In this paper, we…
In this paper we provide a thorough, rigorous theoretical framework to assess optimality guarantees of sampling-based algorithms for drift control systems: systems that, loosely speaking, can not stop instantaneously due to momentum. We…
We consider an optimal transport problem on the unit simplex whose solutions are given by gradients of exponentially concave functions and prove two main results. First, we show that the optimal transport is the large deviation limit of a…
Current LLM alignment techniques use pairwise human preferences at a sample level, and as such, they do not imply an alignment on the distributional level. We propose in this paper Alignment via Optimal Transport (AOT), a novel method for…
This paper shows that the implicit bias of gradient descent on linearly separable data is exactly characterized by the optimal solution of a dual optimization problem given by a smoothed margin, even for general losses. This is in contrast…
We present a new feasible proximal gradient method for constrained optimization where both the objective and constraint functions are given by the summation of a smooth, possibly nonconvex function and a convex simple function. The…
Estimation of origin-destination (OD) demand plays a key role in successful transportation studies. In this paper, we consider the estimation of time-varying day-to-day OD flows given data on traffic volumes in a transportation network for…
We propose an unconstrained optimization method based on the well-known primal-dual hybrid gradient (PDHG) algorithm. We first formulate the optimality condition of the unconstrained optimization problem as a saddle point problem. We then…
We pose the Kantorovich optimal transport problem as a min-max problem with a Nash equilibrium that can be obtained dynamically via a two-player game, providing a framework for approximating optimal couplings. We prove convergence of the…
We present a 2-step optimal transport approach that performs a mapping from a source distribution to a target distribution. Here, the target has the particularity to present new classes not present in the source domain. The first step of…
Applications such as unbalanced and fully shuffled regression can be approached by optimizing regularized optimal transport (OT) distances, such as the entropic OT and Sinkhorn distances. A common approach for this optimization is to use a…
Optimal transport has found numerous applications across data science, many of which require differentiating the optimal transport map with respect to the underlying probability densities in the Fr\'echet sense. In this work, we show that…
Finding optimal trajectories for multiple traffic demands in a congested network is a challenging task. Optimal transport theory is a principled approach that has been used successfully to study various transportation problems. Its usage is…
Recently, researchers proposed various low-precision gradient compression, for efficient communication in large-scale distributed optimization. Based on these work, we try to reduce the communication complexity from a new direction. We…
An equation of Monge-Amp\`ere type has, for the first time, been solved numerically on the surface of the sphere in order to generate optimally transported (OT) meshes, equidistributed with respect to a monitor function. Optimal transport…
The power and flexibility of Optimal Transport (OT) have pervaded a wide spectrum of problems, including recent Machine Learning challenges such as unsupervised domain adaptation. Its essence of quantitatively relating two probability…